Greek Anthology Book XIV: Metrodorus: 141

Arithmetical Epigram of Metrodorus

Tell me the transits of the fixed stars and planets when my wife gave birth to a child yesterday.

It was day, and till the sun set in the western sea it wanted six times two-sevenths of the time since dawn.

Let $t$ be the time since dawn that the birth happened.

It is assumed that the day is $12$ hours long.

We have:

$\ds t$

$=$

$\ds 6 \times \dfrac 2 7 \paren {12 - t}$

$\ds \leadsto \ \ $

$\ds 7 t$

$=$

$\ds 144 - 12 t$

multiplying through by $7$ to clear the fractions and simplifying

$\ds \leadsto \ \ $

$\ds 19 t$

$=$

$\ds 144$

$\ds \leadsto \ \ $

$\ds t$

$=$

$\ds \frac {144} {19}$

$\ds $

$=$

$\ds 7 \frac {11} {19}$

So $7 \frac {11} {19}$ hours had passed since dawn when the baby was born.

That leaves $12 - 7 \frac {11} {19} = 4 \frac 8 {19}$ hours remaining till sunset.

$\blacksquare$

This entry was named for Metrodorus.

1918: W.R. Paton: The Greek Anthology Book XIV ... (previous) ... (next): Metrodorus' Arithmetical Epigrams: $141$